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Showing 1 to 10 of 10 for “"reaction-diffusion equation"”.
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Asymptotic Problems Related to Smoluchowski-Kramers Approximation
… ``Physical" Brownian motion, of the Langevin's equation $\mu\ddot{q}_{t}^{\mu,\varepsilon}=-\dot{q}_{t}^{\mu,\varepsilon}+b(q_{t}^{\mu,\varepsilon})+ \sqrt{\varepsilon}\sigma(q_{t}^{\mu,\varepsilon})\dot{W}_{t},\ q_{0}^{\mu,\varepsilon}=q,\ \dot{q}_{0}^{\mu,\varepsilon}=p$, where $\dot{W}_t$\ is …
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Singularly nonautonomous semilinear evolution equations with almost sectorial operators
… express the fact that the linear part of the equation, A(t) : D X ! X, is time-dependent and the almost sectoriality of the family A(t) comes from a deficiency in its resolvent estimate. For this semilinear problem in the abstract setting we study local well-posedness, regularity of the …
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Sensitivity Enhanced Model Reduction
… techniques are performed on a 1-dimensional reaction-diffusion equation and 2-dimensional incompressible Navier-Stokes equations solved using the finite element method (FEM) as the full scale model. The expanded model formed by expanding the POD basis with the orthonormalized basis …
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History Induced Critical Scaling in Disordered Media and Super Diffusive Growth in Highly Advective Random Environments
… inhomogeneous nutrient concentration. A model reaction-diffusion equation with Fisher growth terms is introduced with a brief discussion of previous work on similar equations and experiments. The linear two-dimensional problem is mapped onto a simplified one-dimensional equation. Numerical …
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Uniform heating of thin ceramic slabs in a multimode microwave cavity
Two-dimensional reaction diffusion equations, which contain a functional and an inhomogeneous source term, are good models for describing microwave heating of thin ceramic slabs and cylinders in a multi mode, highly resonant cavity. A thin ceramic slab situated in a TEN03 rectangular cavity modeled …
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Non-Classical Symmetry Solutions to the Fitzhugh Nagumo Equation.
<p>In <em>Reaction-Diffusion</em> systems, some parameters can influence the behavior of other parameters in that system. Thus reaction diffusion equations are often used to model the behavior of biological phenomena. The Fitzhugh Nagumo partial differential equation is a reaction diffusion …
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A study of the effects of spatially localized time-delayed feedback schemes on spatio-temporal patterns
… transient chaotic states of the Gray-Scott reaction-diffusion system 2) Spatio-temporal patterns emerging from spatially localized time-delayed feedback perturbations within chaotic states of the cubic complex Ginzburg-Landau equation We present an investigation of two model systems: the …
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Some nonlinear problems in plankton ecology
… model without population structure (the Droop equations) does not exhibit this transfer of variability: a periodic nutrient supply produces a periodic population response of exactly the same frequency. In the second part, I consider a predator and a prey that interact and diffuse along an …
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Propagation Failure in Discrete Inhomogeneous Medium Using a Caricature of the Cubic
Spatially discrete Nagumo equations have widespread physical applications, including modeling electrical impulses traveling through a demyelinated axon, an environment typical in multiple scle- rosis. We construct steady-state, single front solutions by employing a piecewise linear reaction term. …
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Modeling of controlled-release drug delivery from autocatalytically degrading polymer microspheres
… effective diffusivity of the drug. A mechanistic reaction-diffusion model with pore evolution coupled to hydrolysis and related to the effective diffusivity through hindered diffusion theory is proposed. Experimental background motivating the attention to the size-dependent effects of …